Named after Archduke Joseph of Austria who was Palatine (Governor) of Hungary from 1796 until he died in Buda in 1847. He tried to modernise Hungary and brought in various reforms and also founded the Hungarian Academy of Sciences. That is his statue (decorated by pigeons) that stands in the square. At the back of the square is the famous Gerbaud House patisserie - one of THE places is Budapest for coffee, cakes and ice-cream.